Papers

We study transient solute dispersion in pressure-driven micropolar flow through a concentric annulus representing a catheterized artery. The catheter is impermeable to solute, whereas the arterial wall combines irreversible removal with reversible surface retention. The exact steady micropolar velocity field is coupled to the Gill-Sankarasubramanian generalized-dispersion framework; the resulting bulk-surface hierarchy is advanced with Rannacher-damped Crank-Nicolson time stepping to determine $K_0(t)$, $K_1(t)$ and $K_2(t)$. The exchange coefficient is independent of the micropolar parameters and satisfies $-K_0(0^+)=2(\beta+\theta Da)/(1-\lambda^2)$, whereas $K_2-Pe^{-2}\sim\sigma_v^2t$ initially, so the leading short-time dispersion is hydrodynamic and independent of wall kinetics. In the weak-reaction regime, micropolarity modifies convection approximately linearly and shear dispersion quadratically through the velocity-amplitude factor. A narrow-gap analysis with $\varepsilon=1-\lambda$ gives $\bar v\sim(2-N_c)\varepsilon^2/6$ and $K_2-Pe^{-2}\sim(2-N_c)^2\varepsilon^6/7560$ for a fixed pressure gradient, revealing a sixth-power suppression of shear dispersion as the catheter approaches the arterial wall. Increasing $\lambda$ from $0.01$ to $0.30$ reduces effective convection by about a factor of $2.45$, while chemically passive shear-induced dispersion falls by a factor of $24$. The coupled formulation also yields the exact partition $\Phi_m+\Phi_s+\Phi_a=1$, separating mobile, reversibly retained and irreversibly absorbed solute. The reconstructed field quantifies reaction-modulated transverse non-uniformity, while the results distinguish hydrodynamic effects of confinement and microrotation from kinetic wall effects.

Three-dimensional flood propagation through the Bhote Koshi–Langtang Khola junction at Syabrubesi, Nepal, is studied using an incompressible free-surface model. The calculation is motivated by the August 2026 flood and examines the passage of an imposed inflow through the local bends and changes in channel width. The Navier–Stokes equations and an interface transport equation are solved on unstructured tetrahedral meshes constructed from pre-event terrain data. For an inlet speed of $10\,\mathrm{m\,s^{-1}}$, the solution indicates surface speeds above $40\,\mathrm{m\,s^{-1}}$. The advancing front spreads across the junction; as the flow develops, water deepens and slows around the bend. Higher speeds persist in the confined upstream and downstream regions.

Time-variable stellar heating may create new climate states, such as permanently hot or cold hemispheres, on asynchronous planets. Planets on eccentric orbits, circumbinary planets and planets on polar orbits around gravity-darkened stars all receive variable irradiation, yet variably irradiated planets (VIPs) have not been studied from a fundamental dynamical perspective. We present the first generalized study of the atmospheric response of variably irradiated tidally locked planets, using a 1.5-layer shallow-water model forced towards a time-dependent radiative equilibrium. We derive linearized analytic expressions for the mean, amplitude and phase lag of the response, which is that of a forced damped harmonic oscillator, and recover the established trends of tidally locked planets in the limit of steady forcing. When the instellation variation and wave timescales match and the damping is weak, a resonance occurs because waves propagate and interfere freely. The resonance produces a global standing wave mode and consequently a temporarily warmer nightside. Linear and nonlinear simulations reproduce these results and show that the hotspot oscillates longitudinally at the forcing frequency and reaches the antistellar point at resonance. The oscillation is eastward or westward of the substellar longitude depending on the rotation rate and the nonlinearity of the system. Synthetic phase curves carry signatures of this variability and invert in shape at resonance because of nightside warming. Among observed systems, we find 11 planets with at least 10% phase curve modulation from variable irradiation. Eccentric, pseudo-synchronous giants are the most promising targets, with HAT-P-2b having the largest predicted modulation.

Turbulent flows are highly chaotic, which makes their instantaneous states difficult to predict. Data assimilation aims to reduce this predictive uncertainty by synthesizing the predictions of a physical solver with partial observations of the system. Traditional data assimilation methods such as ensemble and variational approaches can incur substantial computational cost through evaluations of high-fidelity solvers and, for variational methods, adjoint calculations. Recently, generative diffusion models have been explored in the solution of inverse problems in fluid mechanics, demonstrating their potential for data assimilation. However, existing diffusion-based methods often use free parameters instead of the prescribed observation-error covariance to control the balance between the prior and likelihood, departing from the Bayesian formulation of data assimilation. We propose a framework for principled generative data assimilation in which observations are assimilated in the clean-state space and the prescribed observation-error covariance enters explicitly through an ensemble Kalman update. In the Lorenz-63 system, the proposed method yields a lower trajectory error and equation residual than the other diffusion-based posterior sampling methods considered, although its ensemble underestimates the posterior uncertainty. In two-dimensional Rayleigh-Bénard convection, the generated fields recover the statistics of the direct numerical simulation reference at large scales, with deviations confined to the smaller scales. These results suggest that the framework can produce physically plausible turbulent flow fields, indicating its potential for more challenging turbulent flow applications.

A droplet breaks up in tens of microseconds, and a recording captures perhaps a dozen frames. The states in between cannot be recovered without repeating the experiment, and simulating them is too costly to sweep an operating envelope. Yet they are present in the corpus as a whole: a campaign spanning a device's actuation range produces morphologies resembling those any single recording missed. Exploiting that requires a representation that is low-dimensional, invertible, and faithful to shape rather than to sampling. Proper orthogonal decomposition supplies the first two but measures distance in sampled coordinates; manifold learning supplies the third but no map back to a shape; elastic shape analysis supplies a shape metric but no reduced coordinates. SHROM composes all three. Interfaces are represented by their square-root velocity functions, a neighbour graph is built over that shape space, and an autoencoder is trained to reconstruct while penalising latents in which graph neighbours are not latent neighbours. The demonstration uses 301,539 inkjet droplet contours and four filmed break-up sequences. The graph term does not improve reconstruction. It determines whether position in the latent carries meaning: clustering the latent of an otherwise identical model recovers the shape-space partition at chance level (ARI = 0.063 +/- 0.059), and at 0.781 +/- 0.049 with the term active. Waveform parameters predict the full contour at R^2 = 0.878 +/- 0.026. Negative results are reported in the same terms. The graph metric proved immaterial across five choices, and interpolation error saturates at the reconstruction limit, so a plain autoencoder leads that task. The main limitation is interpolation across a topology change: no component of the regularised latent holds both a single-component and a post-break-up shape, whereas an unregularised autoencoder mixes them freely.

Adsorption and desorption redistribute soluble surfactant between a liquid film and its free surface, but cannot change the total inventory in a closed periodic domain. We audit this requirement in nonlinear weighted-residual models for soluble-surfactant-laden falling films. Although a previous correction restores conservation of the nonlinear surface Marangoni flux, a separate inconsistency remains in the depth-integrated bulk diffusion. We derive the resulting mass imbalance and construct explicit positive periodic concentration fields that exhibit it. The missing contribution arises from the streamwise concentration gradient appearing in the normal diffusive flux at a sloping interface. Including this contribution restores local conservation of the coupled bulk-surface transport system while leaving the hydrodynamic equations, the leading-order adsorption-desorption closure, and the linear stability properties of the uniform equilibrium unchanged. In an independent no-slip calculation using the parameters of an earlier travelling-wave study, the reference model loses $0.0228832\%$ of its initial surfactant mass by $t=4500$, whereas the corrected run has an absolute relative mass change of $1.2\times10^{-15}$. The main hump and capillary ripples remain closely comparable at $t\approx4500$. This benchmark therefore shows that agreement with travelling-wave calculations does not, by itself, guarantee that a reduced model respects the conservation laws inherited from the underlying transport problem. Although the drift is small in this case, the corrected equations conserve the reduced total inventory for every smooth periodic solution. We also distinguish this exact conservation property from higher-order compatibility with the full curved-interface boundary conditions.

Molecular mixing models for the conditional scalar diffusion (CSD) term in the filtered mass density function (FMDF) transport equation used in Large Eddy Simulation (LES-FMDF) approach are evaluated against direct numerical simulation (DNS) of spatially evolving jets. A database of DNS of turbulent mixing slot jets of $C_{7}H_{16} / O_2$ and $C_{7}H_{16} / Air$ is developed. The formulation includes the compressible form of the governing equations, a generalized multicomponent diffusion model, a cubic real gas equation of state and realistic property models. Simulations are conducted over a wide range of initial pressures ($1 atm < P_0 < 100 atm$) and jet width based Reynolds numbers of 850 and 1300. FMDF of mixture fraction at various filter widths are obtained from the simulation at several spatial locations within the flow. The CSD term in the exact transport equation of FMDF is calculated from the DNS. An a priori analysis of Interaction by Exchange of Mean (IEM), Modified Curl (MC) and Mapping Closure (MAPPING) mixing models for CSD is conducted. At high pressures, significant deviations are observed between the CSD measured from the DNS and those predicted by the models. The source of the deviations is determined to be the mixing frequency used in the models. The significance of the mixing frequency and its variation with change in pressure and diffusion models is studied. The primary objective of this work is to assess the applicability of aforementioned mixing models to flows at large pressures and determine the causes for deviation in prediction.

The usage of chemical dispersant to promote the breakup of oil droplets remains one of the crucial response strategy towards controlling the rapidly rising droplets during an underwater oil spillage disaster like the Deepwater horizon. However, the detrimental effects of dispersant on the marine life are now well recognized. Here, we demonstrate that vortex ring presents an environmental friendly alternative to the debatable usage of chemical dispersant that primarily aids droplet break-up. We propose two mitigating strategies through the application of vortex rings: (i) atomization of large oil droplets into smaller droplets, which enhances natural dispersion and biodegradation (ii) targeted relocation of spilled oil droplets from ecologically sensitive regions to safer remote locations during minor spill events. This proof-of-concept study demonstrates that vortex rings can efficiently atomize underwater oil droplets while simultaneously transporting them over long distances. The efficiency strongly depends on the droplet size distribution and the strength of the vortex ring. Using time scale analysis and force balances arguments, we propose droplet response and atomization criteria by a traversing vortex ring. Beyond atomization and droplet transport which are center to many engineering processes, the work finds high relevance in the area of bubble turbulence, agricultural industry, multiphase reactors, combustion process, atmospheric fluid dynamics and oil extraction from rocks, to name a few.

Droplet collision governs droplet population dynamics in many chemical engineering processes, such as spray drying, spray cooling, agricultural spraying, and combustion. Existing analytical models impose deterministic, pairwise boundaries between collision outcomes, whereas machine-learning classifiers lack the explicit functional form required of analytical collision submodels. In this study, we develop a probabilistic symbolic-distillation model using nearly forty thousand experimental events spanning eight regimes and five dimensionless parameters, including over five thousand data for ambient pressure up to 50 atm. A machine-learning teacher learns the joint outcome-probability landscape from these data, and symbolic regression subsequently distils it into eight class-specific expressions that jointly define a coupled analytical model. The resulting analytical field replaces abrupt regime switching with finite-width fuzzy boundaries. It outperforms the evaluated conventional analytical boundary models and reveals that their main limitation is the inability of zero-width boundaries to represent gradual probability transitions. The "biased-dice" sampling scheme provides a statistically consistent and practically convenient model implementation for Eulerian-Lagrangian spray simulation.

We investigate the motion of a spherical microswimmer in a planar Poiseuille flow using analytical calculations and numerical simulations. Our results show that the microswimmer's orientation undergoes periodic oscillations governed by pendulum-like dynamics. The oscillation period is proportional to the channel width and to the complete elliptic integral of the first kind evaluated at the maximum orientation angle, and inversely proportional to the square root of the product of the maximum flow speed and the self-propulsion speed. Based on the net displacement along the flow direction within one oscillation period and the signs of the maximum and minimum velocities, we identify five motion states: upstream, oscillatory upstream, zero-drift oscillatory, oscillatory downstream, and downstream motion. The net displacement is jointly determined by the ratio of the self-propulsion speed to the maximum flow speed and the complete elliptic integrals of the first and second kinds. The signs of the maximum and minimum velocities are determined by the speed ratio and the cosine of the orientation angle. Flow nonuniformity promotes upstream migration, whereas inertial lift produces negligible radial displacement during one oscillation period. These findings identify the key parameters governing the motion of spherical microswimmers and provide significant implications for understanding microorganism motility and designing microrobots with prescribed motion states.

Pressure-driven radial flows of viscoelastic fluids are common in various industrial applications, such as injection molding and extrusion. It is well known that viscoelastic rheology can significantly impact the hydrodynamic features of non-Newtonian flows. However, these hydrodynamic features remain not fully understood compared to those observed in Newtonian flows. We analyze the pressure-driven radial flow of an Oldroyd-B fluid between parallel plates and present a theoretical framework together with finite-element numerical simulations for determining the flow rate-pressure drop relation. Unlike previous theoretical studies restricted to the weakly viscoelastic limit of low Deborah ($De$) numbers, we apply lubrication theory and consider the ultra-dilute limit, which allows us to study viscoelastic radial flows at order-one Deborah numbers. Using the one-way coupling between the Newtonian velocity profile and elastic stresses, we derive closed-form expressions for the conformation tensor and pressure drop in the ultra-dilute limit. We show that the pressure drop monotonically increases with $De$, identify the physical mechanisms governing this increase, and delineate the range of validity of the ultra-dilute approximation. We further reveal that the low-$De$ asymptotic analysis of the pressure drop may fail to accurately capture finite-element simulation results, even at low Deborah numbers, owing to its inability to satisfy the inlet elastic stresses. In contrast, our theoretical predictions based on the ultra-dilute limit are in excellent agreement with the finite-element simulation results, enabling us to elucidate the pressure drop behavior for order-one Deborah numbers.

Porous and perforated leading edges reduce turbulence-interaction noise, but predictions of the reduction have relied on material impedances adjusted to the acoustic data. This paper removes that adjustment. The finite-chord scattering problem is solved in compressible subsonic flow for an arbitrary chordwise admittance, with the shed wake, the Kutta condition and permeability-dependent edge singularities, and closed to the far field with the finite span and the array aperture represented. The admittance of a perforated insert is derived from the Rayleigh conductivity of one aperture with three computed corrections: plate thickness, interaction between neighbouring apertures, and Howe's grazing-flow blockage evaluated at the aperture-averaged velocity of the boundary layer. A bulk porous insert is represented by its measured permeability and pore-fluid inertia. For three perforates at four flow conditions the prediction agrees with measurements to 2.5 dB rms over 84 comparisons, against 4.4 dB with the unscaled impedance used previously. Although the Mach number is 0.05, the chord is acoustically non-compact, and an incompressible solution rises where the measurement falls. Two of three bulk porous inserts are predicted to within 1.7 dB rms where interaction noise dominates. Narrow, equally spaced peaks measured on perforated plates are reproduced by none of the admittances tested; their spacing implies a source convecting at 0.62 of the free-stream speed, absent from a frozen-gust model. A parameter study shows that the perforate geometry acts almost entirely through one low-frequency admittance group, in which the hole radius cancels for holes buried in the laminar boundary layer.

This study investigates generalized boundary representations and transfer learning for physics-informed neural-network (PINN) estimation of spatially varying convective heat transfer coefficients (HTCs) in jet impingement cooling. Piecewise-linear (PWL) and neural-network boundary estimators are inferred from transient interior-temperature measurements and evaluated against CFD-CHT reference HTC profiles at Reynolds numbers of 5000, 10000 and 15000. A discrete Adjoint-FEM formulation with gradient regularization based on the $H^1$-seminorm provides an independent inverse-method comparison. Transfer learning is investigated under two source-target conditions: transfer between noise levels at the same Reynolds number, and transfer from a controlled Gaussian-profile problem to CFD-CHT-derived target problems at different Reynolds numbers. For the representative Re = 5000 target with 5% measurement noise, quadratic, PWL, and neural-network PINNs achieve relative HTC-profile errors of 5.08, 5.31 and 5.19%, respectively, while generalized representations reduce the error for the Re = 15000 target from 16.76% for the quadratic PINN to 14.41% and 14.46%. Transfer learning reduces target-training time by 57.86-81.71% for fixed-Reynolds-number transfer and by 50.59-84.94% for Gaussian-to-CHT transfer. Its effect on reconstruction accuracy is target dependent: fixed-profile PWL transfer remains within 0.30 percentage points of scratch training, whereas Gaussian-to-CHT transfer produces differences of 0.10-1.52 percentage points across targets and representations. These results demonstrate that generalized PINN representations can accommodate spatially varying HTC profiles without a prescribed quadratic form, while transfer learning can substantially reduce target-training cost for repeated inverse estimation, with the resulting reconstruction accuracy depending on source-target compatibility.

The environmental transport of microplastic particles has raised concerns because of their potential ecological and human-health impacts. A particular challenge for experiments on microplastic transport in soils is the fact that soil is a highly complex and non-transparent porous medium. Thus, our knowledge of transport mechanisms of microplastics in soils and related ecological implications is still limited and computational simulations offer an additional possibility to obtain important insights into the physical transport behaviour of microplastics. Yet, direct particle-resolved simulations in realistic soil structures for macroscopic sample sizes remain a computational challenge. We introduce an efficient pore-network model, minD-PNM, that predicts particle breakthrough curves in water-saturated soils using experimental X-ray micro-computed tomography ($\mu$CT) pore geometries as the only input. The model combines an approximately $t^{-3}$ pore-scale transit time distribution with a minimum-dissipation partition of multi-inlet-multi-outlet pores, and propagates these distributions through the pore network to predict breakthrough curves. We benchmark minD-PNM against lattice Boltzmann and immersed boundary simulations for small systems, and against microplastic column experiments in quartz sediments for macroscopic sample sizes. In both cases, the predicted breakthrough curves agree well with the corresponding reference data. Because it requires only geometric information, minD-PNM scales to macroscopic sample volumes offering a practical tool for contaminant-hydrology studies of particulate pollutants.

We present Suêtes, a fully differentiable, non-hydrostatic, limited-area atmospheric dynamical core implemented in JAX. Suêtes includes both a semi-implicit semi-Lagrangian scheme and a Split-Explicit Runge-Kutta scheme with acoustic substepping, enabling applications from coarse regional simulations to convection-permitting dynamics. Its terrain-following geometry, spatial discretization, time integration, initial conditions, lateral boundary treatment, and included physical parameterizations are all compatible with reverse-mode automatic differentiation. A single reverse-mode pass can therefore compute sensitivities of forecast diagnostics to selected initial and boundary fields, physical parameters, topography, and computational geometry. We provide a series of numerical experiments—including a tracer-source inverse problem, a sensitivity analysis of a three-dimensional squall-line, adversarial perturbation construction an ERA5-driven downslope hurricane force wind event, topography optimization, and terrain-following coordinate optimization—demonstrating the versatility of Suêtes as a framework for gradient-based diagnosis and model development at regional and convection-permitting scale.

Transporting droplets along cylindrical surfaces is an emerging area of research with a wide range of practical applications such as fog collection and filtration. Recent experimental studies by Feng et al. (2024) have revealed a wealth of new droplet coalescence dynamics on a pre-wetted cylindrical fibre, illustrating the need for more advanced theory. In this paper, we study both the early-stage and late-stage dynamics of droplet coalescence on a sloped cylindrical fibre. In the early stage, when the minimum thickness of the liquid bridge connecting two droplets is small, we propose a lubrication-based model to analyze the capillary-driven self-similar dynamics of the liquid bridge. Our theory predicts the bridge growth rate and demonstrates that asymmetry in the adjoining contact angles contributes to the migration of the merged droplet, showing good agreement with experimental observations. In the late stage, as droplet merging progresses, inertia effects become significant and lead to rapid mass transfer. To capture this regime, we develop a weighted residual model for liquid films flowing on a sloped pre-wetted cylinder, incorporating key physical effects such as gravity, low-to-moderate inertia, surface tension, and intermolecular forces. This model explains the experimentally observed directional self-propelled transport during droplet coalescence, where the larger droplet migrates toward the smaller one. Numerical simulations based on this model further support these findings, showing good agreement between the predicted coalescence-induced droplet migration and experimental observations.

Odd pressure is a parity-odd transport coefficient that gives an isotropic pressure response to vorticity in compressible two-dimensional fluids. By asymmetrically coupling vortical and compressional modes, it provides a direct mechanism for a nonreciprocal hydrodynamic response reminiscent of several biological systems. Yet microscopic models realizing odd pressure as a transport coefficient are relatively scarce. Here, we construct one such model using a lattice-gas cellular automaton based on the Frisch-Hasslacher-Pomeau II model with rest particles and chiral collisions, whose Chapman-Enskog coarse-graining produces a nonzero odd pressure coefficient. The key ingredient is a local parity-breaking collision that weakly rotates moving particles in the presence of a rest particle. At hydrodynamic scales, this microscopic rule acts as an effective magnetic field, converting the model's bulk viscosity into odd pressure. More generally, we derive expressions relating Hall viscosity, odd pressure, and odd torque to their parity-even counterparts in our model.

We formulate a scale dependent tensorial extension of a fractional dissipation operator motivated by a macroscopic Navier Stokes correspondence. The starting point is a fractional model in which the order of dissipation decreases continuously from the Laplacian value toward the Kolmogorov value as a local Reynolds number increases. At the critical value of the local Reynolds number, the model reduces to an isotropic operator. We then ask whether the same macroscopic description can be continued into a regime in which velocity fields have Onsager, critical or subcritical regularity without introducing an unrelated closure or an additional isotropic dissipation scale. In addition, we extend the original AFNS free, energy, construction by one nonnegative concentration order parameter c. The new term is quadratic in c and linearly coupled to the defect beta function, so that minimization leaves the original AFNS free energy exactly unchanged when the concentration branch is inactive. The resulting three regime mosaic is regular, inertial, and concentrated/anomalous. The construction uses the coarse-grained stress and its critical normalization. The normalized anisotropy tensor provides the lowest order objective tensorial information available at the critical scale, while the scale derivative of the Duchon Robert energy defect, supplies a scalar measure of departure from the Onsager threshold. We propose the minimal constitutive deformation of the critical operator: in Weyl quantization, the isotropic fractional symbol is dressed by this exponential tensorial factor, giving a pseudodifferential operator that reduces to the scalar critical operator. The exponential parametrization guarantees positive eigenvalues and unit determinant for symmetric traceless, so the deformation redistributes dissipation among directions without introducing a new isotropic amplitude.

We present a conservative local grid-refinement coupling for the vectorial lattice Boltzmann method (VLBM), a kinetic-type scheme for hyperbolic conservation laws in which each conserved field is carried by its own population rather than by moment truncation of a Maxwellian. Coarse and fine regions share a common link speed and are advanced with different time steps, sub-cycled at a fixed ratio; a mean-preserving reconstruction in time supplies the missing coarse-to-fine boundary data, and a matched, Berger–Colella-style reflux returns the fine-to-coarse data, together conserving mass, momentum, and energy exactly, independent of the equation of state, the local relaxation parameter, or the time step. In addition, we propose an adaptive mesh refinement extension through a conservative pair of splitting and merging operators that require no modification to the underlying coupling. The approach is validated on a sequence of increasingly demanding two-dimensional cases, in every case recovering exact conservation and the expected accuracy gains over an equivalent uniform grid.

Multiscale gas flows often span a wide range of Knudsen numbers, within which the flow varies from near-continuum to highly rarefied and strongly nonequilibrium states. Such flows require kinetic solvers that remain accurate across the entire range. The discrete unified gas-kinetic scheme (DUGKS) provides such a unified description, but its computational cost and memory consumption are dominated by the size of the discrete velocity space. To alleviate this bottleneck, this work improves the DUGKS with multi-level adaptive velocity-space discretization (MLVS-DUGKS), reducing velocity-space redundancy while preserving accuracy and conservation. This method identify the velocity-space requirements of each physical cell from its distribution function, and then groups these requirements into a small number of representative velocity spaces. This organization retains sensitivity to different local flow states without constructing an independent velocity space for every physical cell. A linear moment-constrained correction is incorporated to maintain discrete compatibility and conservative data transfer between representative velocity spaces. Benchmark simulations spanning near-continuum to highly rarefied regimes show close agreement with the uniform-velocity-space DUGKS (UVS-DUGKS). For the computationally demanding cases, the average number of discrete velocity points is reduced by approximately one order of magnitude, yielding speedups of 6.67–7.51 and GPU-memory reductions by factors of 6.15–6.88. A threshold study further shows that the actual computational performance is governed by a balance between velocity-space compression and cross-level coupling overhead. The MLVS-DUGKS thus provides an accurate, conservative, and computationally efficient framework for multiscale nonequilibrium-flow simulations.

Dimensionless descriptions of complex physical systems can sometimes be reduced further when multiple input groups combine into a single composite scaling coordinate. Identifying such structure from noisy response evaluations is difficult because apparent departures may reflect either genuine response structure or evaluation noise. Here we develop equal-response probing with replicate calibration to assess whether two dimensionless inputs support a one-group representation under prescribed directional and collapse tolerances. Equal-response geometry provides a candidate coordinate without direct numerical differentiation, while a second stage evaluates the accuracy of the resulting one-dimensional collapse. Replicate evaluations estimate the noise contribution to both stages, enabling reducible, not-red and unresolved outcomes. We evaluate the framework across eight model-based benchmark regimes spanning rough-pipe flow, cell-monolayer wound closure, microfluidic droplet generation and column buckling. Six regimes satisfy both criteria and two fail both, while known reduced coordinates are recovered in exact-reduction benchmarks. Controlled synthetic tests assess false-alarm behaviour, sensitivity to structural departures and noise calibration. These results show how replicate-calibrated equal-response probing distinguishes regime-specific scaling structure from variation attributable to evaluation noise while retaining an unresolved outcome when evaluation noise precludes a definitive verdict at the prescribed tolerances.

We present an enhancement of classical immersed boundary methods for the direct numerical simulation of the incompressible Navier-Stokes equations, designed to efficiently cope with geometrical singularities. The method, while general, is described here in the context of the flow over a plane wall covered by small longitudinal riblets. The enhancement consists in prescribing that the solution near the boundary matches the steady Stokes solution. In this way, sharp corners, where velocity gradients are strongest and viscous effects dominate, become tractable with grids comparable to those necessary for a smooth wall. The method requires the availability of a local Stokes solution, that can be obtained either analytically or numerically. Two test cases are discussed: the laminar flow over one riblet, which allows to measure protrusion heights, and a fully turbulent channel flow with ribbed walls. In both cases, the method reproduces reference results at a substantially lower computational cost.

Predictions of moving contact line flows are challenging due to the stress singularity associated with the no-slip boundary condition on solid surfaces and the inherently multiscale nature of the phenomenon. Resolving the microscopic length scale renders the numerical simulations intractable for macroscopic flows due to extremely high computational costs. Affordable and predictive numerical solutions for macroscopic flows require a subgrid model, free of case-specific calibration, that mitigates the grid-dependence observed otherwise. We demonstrate a coupling between Cox's matched asymptotic relation and the empirical contact angle models to obtain a quasi-universal subgrid model. The coupling requires a one-time knowledge of the observation length scale or resolution of the experiments used to formulate the empirical models. The present model eliminates the need for prescribing phenomenological parameters such as the microscopic slip length and wall contact angle, allowing for the predictive simulations of such flows. We demonstrate the reduction in error due to grid-dependence by conducting axisymmetric simulations of droplet spreading for a wide range of Reynolds and Weber numbers for three different contact angle models in the advancing and receding contact line motion scenarios.

Accurate prediction of avalanche motion is essential for hazard assessment in mountainous terrain. This study develops and evaluates a physics-informed neural network (PINN) framework for the Savage-Hutter model of depth-averaged granular flow, progressing from 1D analytical verification to 2D experimental validation. First, three 1D problems of increasing complexity were verified against the analytical solution: height prediction with prescribed velocity, velocity prediction with prescribed height, and coupled prediction of both fields using the conservative formulation. The decoupled tests accurately reconstructed the spatio-temporal evolution of each field when the other was prescribed. The coupled formulation learned both fields without prescribed data, achieving mean height and velocity RMSEs of 0.043 and 0.079 in non-dimensional units. A hyperparameter sensitivity study evaluated the effects of network depth, width, collocation density, learning rate, and epochs. The framework was then extended to 2D and validated against laboratory experiments of a cylindrical granular pile collapsing on an inclined plane, with TITAN2D providing numerical comparisons. Purely physics-based training converged to the trivial zero solution; augmenting the loss with 10 sparse training points from final deposit profiles produced a physics-informed, data-assisted hybrid framework. Peak flow depth, depth-averaged velocity, RMSE, and wetted-area IoU evaluated global and local agreement. Global height RMSE ranged from 2.7 to 6.7 mm across four experimental cases, while mean wetted-area IoU ranged from 69 to 81 %, demonstrating consistent performance across variations in pile mass and slope angle.

Many process engineering applications hold a gas-liquid interface stationary inside a structured solid by a controlled pressure difference. Gas diffusion electrodes (GDEs) are one such case, where the interface separates the liquid electrolyte from the gaseous reactant. Maintaining it is particularly challenging in organic electrosynthesis, where low surface tensions lower the admissible pressures throughout and small contact angles leave the electrode with little margin against flooding. Here, we quantify how the shape, wettability, and three-dimensional topology of a structured medium set this window, using phase-field simulations of the Cahn-Hilliard-Navier-Stokes equations. Each geometry is characterised by its Laplace pressure curve, which yields both the maximum admissible pressure difference and the stiffness of the interface against pressure fluctuations. For single flat orifices at constant open area, elongating the opening from an aspect ratio of one to six raises the admissible pressure difference by 40 % and the stiffness by a factor of 3.3. Comparison with slits of equal width shows that this gain originates entirely from the reduced opening width. Sheared, diamond shaped openings are markedly less effective. In woven meshes, the wettability displaces the operating window several times as far as it stretches it. A less wetting surface therefore buys flooding margin largely at the expense of breakthrough margin, whereas the geometric route, established here for flat openings, widens the window itself. From these results we derive design rules for structured gas-liquid contactors and improved GDE architectures for organic electrosynthesis.

The pseudo-parabolic term $u_{xxt}$ serves as a canonical example of higher-order viscosity that provides effective regularization while capturing the refined physical mechanism. How it alters the dynamics of prototype equations remains a fundamental issue, which is not yet fully understood. The goal of this paper is to show that this term induces a sharp transition in traveling wave structure, via studying the pseudo-parabolic Fisher-KPP equation $$ u_t - \tau u_{xxt} = D u_{xx} + u(1-u). $$ We completely characterize how the parameter ratio $\tau/D$ acts as a critical switch: it preserves the monotonic structure of classical traveling waves when $\tau/D \leq 1$, yet it triggers a qualitative shift to oscillatory traveling waves when $\tau/D > 1$. Numerical simulations support these findings. The threshold $\tau/D=1$ thus captures the dual role of the pseudo-parabolic term: it acts as a structure-preserving viscosity when small, but when large it reflects dominant capillary hysteresis, generating the oscillations that explain the saturation overshoot, a phenomenon that contradicts classical diffusion models yet is widely observed in two-phase flow.

We present a formulation for the linear stability of the miscible Rayleigh-Taylor instability, retaining viscosity, Fickian mass diffusion, and non-Boussinesq effects. Rather than adopting the diffusive corrections of Duff, Harlow, and Hirt (1962) or relying on the viscous eigenvalue problem of Chandrasekhar (1961), the present formulation is derived directly from the incompressible variable-density governing equations. Both approaches are recovered as limiting cases, extending Morgan, Likhachev, and Jacobs (2016). The governing equations admit a time-evolving self-similar diffusive base state in which an error-function density profile is accompanied by a nonzero vertical base velocity required by the non-solenoidal constraint. Linearization yields a reduced coupled formulation for the vertical velocity and density perturbations, suitable for both theoretical analysis and computation. Within the quasi-steady-state approximation, we show that the formulation reduces, in the infinite-Schmidt-number limit, to the classical viscous immiscible theory and recovers the Chandrasekhar eigenvalue problem. At finite Schmidt number, diffusion alters the growth-rate spectrum and its high-wavenumber structure. Beyond the spectral cutoff we establish the scaling $\omega_r \sim -\lambda_m k^2$, where $\lambda_m$ is determined by the competition between the locally stratified kinematic viscosity and the reference diffusive scale. By isolating the effect of diffusion, we show that its stabilizing influence weakens with increasing density stratification. Buoyancy production becomes bimodal and shifts toward the lighter-fluid side, while pressure production grows to rival buoyancy and acts as an energy source on the heavier side of stratification. Together, these results clarify when classical diffusive corrections remain applicable and when diffusion and non-Boussinesq coupling must be retained.

The wave-particle decomposition of kinetic relaxation equations is extended to the full Boltzmann equation. An identity transformation writes the collision term as a relaxation toward the local Maxwellian plus a conservative remainder. Along characteristics, the equilibrium integral over a local kinetic horizon defines the wave, and its exact complement, the particle, carries the remainder. The moments of the wave and particle equations are extended Navier-Stokes equations, and the total conservation law and the particle equation form the wave-particle multiscale equations, a closed system, exact for every horizon, that spans a continuous spectrum from the Boltzmann equation to Navier-Stokes hydrodynamics, parametrized by the horizon-to-relaxation ratio. A coupled implicit wave-particle iteration solves this system, updating the conservative variables with the particle fixed and the particle with the predicted wave and an endpoint traction from the macroscopic prediction. Under discrete compatibility assumptions the iteration preserves the discrete Boltzmann solution as its fixed point, and its near-continuum convergence factor is bounded by a particle transport share decaying exponentially with this ratio. Tests on a normal shock, Couette and cavity flows, and hypersonic cylinder and Apollo flows agree with the conventional iterative scheme in rarefied and transition regimes and with Navier-Stokes solutions near the continuum limit. There the wave-particle iteration needs about three to more than four orders of magnitude fewer iterations than this scheme or, where it did not converge, its Shakhov version, and the Boltzmann solution costs one to four times the wall time of a Navier-Stokes solver on the same mesh.

Divergence-free vector fields are fundamental state variables in incompressible flows and many PDE systems. Redundant parameterizations, including Neural Conservation Law (NCL) potentials, map multiple auxiliary representations to the same physical field. Our experiments show that this redundancy can reduce static representation-fitting error by enlarging the set of equivalent solutions, but the resulting many-to-one mapping does not provide a unique state for operator learning. We introduce a minimal representation that encodes a real \(D\)-component divergence-free vector field on a \(D\)-dimensional domain as a real \((D-1)\)-component field on the same domain. Exploiting the transverse structure imposed by incompressibility in Fourier space, we use a Householder orthogonal transformation to construct the reduced coordinates directly. For periodic and closed impermeable fields, the transform is invertible, isometric, and angle-preserving. For open nonperiodic flows, Fourier extension constructs a compatible periodic field, and a minimum-energy rule selects a unique reduced representation. Neural operators then learn temporal evolution entirely in this reduced space. At inference, the predicted \((D-1)\)-component field is decoded directly into a physical divergence-free \(D\)-component field, without predicting an ambient field or applying post-hoc projection. Experiments on static fitting and temporal prediction reveal a task-dependent trade-off: redundancy facilitates static optimization, whereas unique invertible coordinates provide a well-defined state for temporal dynamics. By removing unconstrained longitudinal or null directions from the learned state space, the proposed formulation achieves lower prediction error and greater robustness while preserving divergence freedom by construction.

In many turbulent flows, the quantities of interest are coarse-grained variables, either because resolving the fine scales is computationally prohibitive or because only coarse observations are available; in both cases, data-driven reduced-order models that evolve only these variables are required. Even when the governing equations are known, their projection onto the coarse variables is not closed, and the central difficulty lies in representing the feedback of the unresolved scales so that the reduced model reproduces the statistical and dynamical properties of the projected high-resolution system. We address this problem with a score-based framework, constructing a reduced-order model of quasi-geostrophic turbulence whose stationary distribution coincides by construction with the distribution learned from data and whose dynamics are calibrated to reproduce the finite-time correlations of the energies in individual wavenumber shells. The resulting model reproduces the stationary statistics of the resolved flow with high accuracy, and its calibration is computationally inexpensive because it requires no forward integration of the model.